Challenging the $\omega_0\omega_a$CDM parametrization through rational expansions in view of DESI data release

In view of the new Dark Energy Spectroscopic Instrument (DESI) 2025 results, we analyze three types of \emph{Pad\'e cosmology}, based on rational series making use of Pad\'e approximants over the equations of state, namely Pad\'e$^{\omega}$ (0,1) and Pad\'e$^{\omega}$ (1,1), plus a Pad\'e$^{q}$ (0,1), i.e., a rational expansion on the dark energy deceleration parameter, in which where the numerator and denominator orders are incorporated into the above brackets. These scenarios appear alternative dark energy parameterizations with respect to the well-known $\omega_0\omega_a$CDM model, claimed as the most viable model by DESI. Accordingly, we perform Monte Carlo Markov chain (MCMC) analyses with the publicly available \texttt{CLASS} Boltzmann code, including the three Pad\'e cosmology, along with the $\omega_0\omega_a$CDM and $\Lambda$CDM standard pictures. To this end, we combine independent probes from high to low redshifts to obtain reliable constraints on the cosmological parameters of these models and compare them using statistical selection criteria. \emph{Our results show that Pad\'e cosmology is neither statistically excluded nor worse than the $\omega_0\omega_a$CDM parametrization}. On the contrary, the Akaike Information Criterion (AIC) identifies Pad\'e$^{q}$ (0,1) as \emph{the best-fit model}, with weak evidence against the $\omega_0\omega_a$CDM parameterization, while the Deviance Information Criterion (DIC) provides \emph{strong evidence against the $\omega_0\omega_a$CDM model, favoring Pad\'e (1,1)}. Based on our bounds, we further investigate the evolution of the squared sound speed, revealing that the Pad\'e$^{q}$ (0,1) and Pad\'e$^{\omega}$ (0,1) parameterizations exhibit enhanced stability compared with the other cases here considered and, therefore, describe robust alternatives for the cosmological background.